P.3.7.4.1 Capacitance

The graph shows the variation of potential difference (pd) with charge for a capacitor while it is charging. Which statement can be deduced from the graph?

• The charging current is constant.

• The energy stored in the capacitor increases uniformly with time.

• The capacitance of the capacitor is constant.

• The power supply used to charge the capacitor had a constant terminal pd.

Initially a capacitor stores 600 µC of charge. When it loses half of this charge, the potential difference (pd) across it decreases by 50 V. What is the capacitance of the capacitor?

• 1.5 µF

• 3.0 µF

• 6.0 µF

• 12 µF

Which of the following statements about a parallel plate capacitor is incorrect?

• The capacitance of the capacitor is the amount of charge stored by the capacitor when the pd across the plates is 1 V.

• A uniform electric field exists between the plates of the capacitor.

• The charge stored on the capacitor is inversely proportional to the pd across the plates.

• The energy stored when the capacitor is fully charged is proportional to the square of the pd across the plates.

A variable capacitor has a capacitance which can be varied from 6.0 × 10^–12 F to 3.0 × 10^–12 F. The capacitor is set to its maximum capacitance and fully charged using a 48 V supply. The capacitor is then disconnected from the supply and isolated. Finally the capacitance is reduced to its minimum value without any charge being lost by the capacitor.

Which line, A to D, in the table correctly shows the potential difference (pd) across the capacitor and the charge it stores after the capacitance has been reduced?

• A

• B

• C

• D

An uncharged 4.7 nF capacitor is connected to a 1.5 V supply and becomes fully charged. How many electrons are transferred to the negative plate of the capacitor during this charging process?

• 2.2 × 10¹⁰

• 3.3 × 10¹⁰

• 4.4 × 10¹⁰

• 8.8 × 10¹⁰

A capacitor of capacitance 10 μF is charged through a resistor R to a potential difference (pd) of 20 V using the circuit shown. When the capacitor is fully charged which one of the following statements is incorrect?

• The energy stored by the capacitor is 2 mJ.

• The total energy taken from the battery during the charging process is 2 mJ.

• The pd across the capacitor is 20 V.

• The pd across the resistor is 0 V.

The diagram shows a rigidly-clamped straight horizontal current-carrying wire held mid-way between the poles of a magnet on a top-pan balance. The wire is perpendicular to the magnetic field direction. The balance, which was zeroed before the switch was closed, read 161 g after the switch was closed. When the current is reversed and doubled, what would be the new reading on the balance?

• −322 g

• −161 g

• zero

• 322 g

An initially uncharged capacitor of capacitance 20 μF is charged by a constant current of 80 μA. Which line, A to D, in the table gives the potential difference across, and the energy stored in, the capacitor after 50 s?

• A

• B

• C

• D

Which one of the following statements about a parallel plate capacitor is incorrect?

• The capacitance of the capacitor is the amount of charge stored by the capacitor when the pd across the plates is 1V.

• A uniform electric field exists between the plates of the capacitor.

• The charge stored on the capacitor is inversely proportional to the pd across the plates.

• The energy stored when the capacitor is fully charged is proportional to the square of the pd across the plates.

A 1000 μF capacitor and a 10 μF capacitor are charged so that they store the same energy. The pd across the 1000 μF capacitor is V₁ and the pd across the other capacitor is V₂.

What is the value of the ratio (V₁/V₂)² ?

• 1/1000

• 1/100

• 1/10

• 10